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D.2.4.11 addcons

Procedure from library grobcov.lib (see grobcov_lib).

Usage:
addcons( ( ( (p1_1,(p1_11,..,p1_1k_1).. (p1_s,(p1_s1,..,p1_sk_s)),.., ( (pn_1,(pn_11,..,pn_1j_1).. (pn_s,(pn_s1,..,pn_sj_s)) ) ) a list L of locally closed sets in P-representation

Return:
the canonical P-representation of the constructible set of the union.

Note:
It is called internally by the routines locus, locusdg,

Example:
 
LIB "grobcov.lib";
ring R=(0,a,b),(x1,y1,x2,y2,p,r),dp;
ideal S93=(a+1)^2+b^2-(p+1)^2,
(a-1)^2+b^2-(1-r)^2,
a*y1-b*x1-y1+b,
a*y2-b*x2+y2-b,
-2*y1+b*x1-(a+p)*y1+b,
2*y2+b*x2-(a+r)*y2-b,
(x1+1)^2+y1^2-(x2-1)^2-y2^2;
short=0;
"System S93="; S93; " ";
==> System S93=
==> S93[1]=-p^2-2*p+(a^2+2*a+b^2)
==> S93[2]=-r^2+2*r+(a^2-2*a+b^2)
==> S93[3]=(-b)*x1+(a-1)*y1+(b)
==> S93[4]=(-b)*x2+(a+1)*y2+(-b)
==> S93[5]=-y1*p+(b)*x1+(-a-2)*y1+(b)
==> S93[6]=-y2*r+(b)*x2+(-a+2)*y2+(-b)
==> S93[7]=x1^2+y1^2-x2^2-y2^2+2*x1+2*x2
==>  
def GC93=grobcov(S93);
"grobcov(S93)="; GC93; " ";
==> grobcov(S93)=
==> [1]:
==>    [1]:
==>       _[1]=1
==>    [2]:
==>       _[1]=1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=0
==>          [2]:
==>             [1]:
==>                _[1]=(8*a^10+41*a^8*b^2-56*a^8+84*a^6*b^4-164*a^6*b^2+144*\
   a^6+86*a^4*b^6-148*a^4*b^4+86*a^4*b^2-176*a^4+44*a^2*b^8-28*a^2*b^6-148*a\
   ^2*b^4+156*a^2*b^2+104*a^2+9*b^10+12*b^8-74*b^6-172*b^4+137*b^2-24)
==>             [2]:
==>                _[1]=(b)
==>             [3]:
==>                _[1]=(a)
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=r
==>       _[2]=p
==>       _[3]=y2
==>       _[4]=x2
==>       _[5]=y1
==>       _[6]=x1
==>    [2]:
==>       _[1]=(384*b^6+16768*b^4-11776*b^2+2048)*r+(-24*a^9*b^2+32*a^9-24*a^\
   8*b^4-1240*a^8*b^2+416*a^8-51*a^7*b^4+2132*a^7*b^2-832*a^7-99*a^6*b^6-497\
   1*a^6*b^4+7236*a^6*b^2-1856*a^6-3*a^5*b^6+6109*a^5*b^4-10364*a^5*b^2+3072\
   *a^5-153*a^4*b^8-7560*a^4*b^6+13805*a^4*b^4-13740*a^4*b^2+3328*a^4+51*a^3\
   *b^8+6118*a^3*b^6-10497*a^3*b^4+15772*a^3*b^2-4800*a^3-105*a^2*b^10-5179*\
   a^2*b^8+7369*a^2*b^6-6425*a^2*b^4+12844*a^2*b^2-3776*a^2+27*a*b^10+2133*a\
   *b^8-691*a*b^6-7977*a*b^4-9820*a*b^2+4576*a-27*b^12-1350*b^10+396*b^8+286\
   6*b^6-20305*b^4+13076*b^2-2208)
==>       _[2]=(384*b^6+16768*b^4-11776*b^2+2048)*p+(-24*a^9*b^2+32*a^9+24*a^\
   8*b^4+1240*a^8*b^2-416*a^8-51*a^7*b^4+2132*a^7*b^2-832*a^7+99*a^6*b^6+497\
   1*a^6*b^4-7236*a^6*b^2+1856*a^6-3*a^5*b^6+6109*a^5*b^4-10364*a^5*b^2+3072\
   *a^5+153*a^4*b^8+7560*a^4*b^6-13805*a^4*b^4+13740*a^4*b^2-3328*a^4+51*a^3\
   *b^8+6118*a^3*b^6-10497*a^3*b^4+15772*a^3*b^2-4800*a^3+105*a^2*b^10+5179*\
   a^2*b^8-7369*a^2*b^6+6425*a^2*b^4-12844*a^2*b^2+3776*a^2+27*a*b^10+2133*a\
   *b^8-691*a*b^6-7977*a*b^4-9820*a*b^2+4576*a+27*b^12+1350*b^10-396*b^8-286\
   6*b^6+20305*b^4-13076*b^2+2208)
==>       _[3]=(192*b^11+7232*b^9-54464*b^7+111808*b^5-59136*b^3+9216*b)*y2+(\
   192*a^9*b^6-88*a^9*b^4-1656*a^9*b^2+576*a^9-24*a^8*b^8+344*a^8*b^6-1480*a\
   ^8*b^4+2184*a^8*b^2-576*a^8+768*a^7*b^8-619*a^7*b^6-9031*a^7*b^4+13080*a^\
   7*b^2-3456*a^7-75*a^6*b^10+2179*a^6*b^8-12769*a^6*b^6+26265*a^6*b^4-17784\
   *a^6*b^2+3456*a^6+1149*a^5*b^10-17*a^5*b^8-16409*a^5*b^6+26589*a^5*b^4-27\
   000*a^5*b^2+6912*a^5-78*a^4*b^12+4343*a^4*b^10-30203*a^4*b^8+76341*a^4*b^\
   6-80787*a^4*b^4+40248*a^4*b^2-6912*a^4+762*a^3*b^12+1525*a^3*b^10-11113*a\
   ^3*b^8-11713*a^3*b^6+30379*a^3*b^4+7560*a^3*b^2-5760*a^3-27*a^2*b^14+3603\
   *a^2*b^12-25042*a^2*b^10+58738*a^2*b^8-57019*a^2*b^6+41515*a^2*b^4-26664*\
   a^2*b^2+5760*a^2+189*a*b^14+999*a*b^12-2*a*b^10-23630*a*b^8+43749*a*b^6-4\
   8233*a*b^4+8016*a*b^2+1728*a+1107*b^14-6237*b^12-1554*b^10+62550*b^8-1079\
   85*b^6+38679*b^4+2016*b^2-1728)
==>       _[4]=(192*b^10+7232*b^8-54464*b^6+111808*b^4-59136*b^2+9216)*x2+(-2\
   4*a^9*b^6+536*a^9*b^4-1568*a^9*b^2+528*a^9-240*a^8*b^6+1520*a^8*b^4-2640*\
   a^8*b^2+720*a^8-75*a^7*b^8+2947*a^7*b^6-13388*a^7*b^4+17234*a^7*b^2-4704*\
   a^7-942*a^6*b^8+7022*a^6*b^6-17050*a^6*b^4+14442*a^6*b^2-3168*a^6-78*a^5*\
   b^10+5492*a^5*b^8-30220*a^5*b^6+59932*a^5*b^4-54198*a^5*b^2+13248*a^5-138\
   0*a^4*b^10+10366*a^4*b^8-27206*a^4*b^6+32970*a^4*b^4-23886*a^4*b^2+5184*a\
   ^4-27*a^3*b^12+4365*a^3*b^10-23517*a^3*b^8+47625*a^3*b^6-68732*a^3*b^4+71\
   894*a^3*b^2-19104*a^3-894*a^2*b^12+5758*a^2*b^10-12692*a^2*b^8+20772*a^2*\
   b^6-42670*a^2*b^4+37374*a^2*b^2-8352*a^2+1296*a*b^12-5238*a*b^10-1556*a*b\
   ^8+38920*a*b^6-64236*a*b^4-9554*a*b^2+10032*a-216*b^14+918*b^12-2274*b^10\
   +10828*b^8-13276*b^6-24370*b^4+20022*b^2-3600)
==>       _[5]=(192*b^11+7232*b^9-54464*b^7+111808*b^5-59136*b^3+9216*b)*y1+(\
   -192*a^9*b^6+88*a^9*b^4+1656*a^9*b^2-576*a^9-24*a^8*b^8+344*a^8*b^6-1480*\
   a^8*b^4+2184*a^8*b^2-576*a^8-768*a^7*b^8+619*a^7*b^6+9031*a^7*b^4-13080*a\
   ^7*b^2+3456*a^7-75*a^6*b^10+2179*a^6*b^8-12769*a^6*b^6+26265*a^6*b^4-1778\
   4*a^6*b^2+3456*a^6-1149*a^5*b^10+17*a^5*b^8+16409*a^5*b^6-26589*a^5*b^4+2\
   7000*a^5*b^2-6912*a^5-78*a^4*b^12+4343*a^4*b^10-30203*a^4*b^8+76341*a^4*b\
   ^6-80787*a^4*b^4+40248*a^4*b^2-6912*a^4-762*a^3*b^12-1525*a^3*b^10+11113*\
   a^3*b^8+11713*a^3*b^6-30379*a^3*b^4-7560*a^3*b^2+5760*a^3-27*a^2*b^14+360\
   3*a^2*b^12-25042*a^2*b^10+58738*a^2*b^8-57019*a^2*b^6+41515*a^2*b^4-26664\
   *a^2*b^2+5760*a^2-189*a*b^14-999*a*b^12+2*a*b^10+23630*a*b^8-43749*a*b^6+\
   48233*a*b^4-8016*a*b^2-1728*a+1107*b^14-6237*b^12-1554*b^10+62550*b^8-107\
   985*b^6+38679*b^4+2016*b^2-1728)
==>       _[6]=(192*b^10+7232*b^8-54464*b^6+111808*b^4-59136*b^2+9216)*x1+(-2\
   4*a^9*b^6+536*a^9*b^4-1568*a^9*b^2+528*a^9+240*a^8*b^6-1520*a^8*b^4+2640*\
   a^8*b^2-720*a^8-75*a^7*b^8+2947*a^7*b^6-13388*a^7*b^4+17234*a^7*b^2-4704*\
   a^7+942*a^6*b^8-7022*a^6*b^6+17050*a^6*b^4-14442*a^6*b^2+3168*a^6-78*a^5*\
   b^10+5492*a^5*b^8-30220*a^5*b^6+59932*a^5*b^4-54198*a^5*b^2+13248*a^5+138\
   0*a^4*b^10-10366*a^4*b^8+27206*a^4*b^6-32970*a^4*b^4+23886*a^4*b^2-5184*a\
   ^4-27*a^3*b^12+4365*a^3*b^10-23517*a^3*b^8+47625*a^3*b^6-68732*a^3*b^4+71\
   894*a^3*b^2-19104*a^3+894*a^2*b^12-5758*a^2*b^10+12692*a^2*b^8-20772*a^2*\
   b^6+42670*a^2*b^4-37374*a^2*b^2+8352*a^2+1296*a*b^12-5238*a*b^10-1556*a*b\
   ^8+38920*a*b^6-64236*a*b^4-9554*a*b^2+10032*a+216*b^14-918*b^12+2274*b^10\
   -10828*b^8+13276*b^6+24370*b^4-20022*b^2+3600)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(8*a^10+41*a^8*b^2-56*a^8+84*a^6*b^4-164*a^6*b^2+144*a^6\
   +86*a^4*b^6-148*a^4*b^4+86*a^4*b^2-176*a^4+44*a^2*b^8-28*a^2*b^6-148*a^2*\
   b^4+156*a^2*b^2+104*a^2+9*b^10+12*b^8-74*b^6-172*b^4+137*b^2-24)
==>          [2]:
==>             [1]:
==>                _[1]=(b)
==>                _[2]=(a-1)
==>             [2]:
==>                _[1]=(b)
==>                _[2]=(a+1)
==>             [3]:
==>                _[1]=(b)
==>                _[2]=(a^2-3)
==>             [4]:
==>                _[1]=(b^4+44*b^2-16)
==>                _[2]=(5*a-b^2-7)
==>             [5]:
==>                _[1]=(b^4+44*b^2-16)
==>                _[2]=(5*a+b^2+7)
==>             [6]:
==>                _[1]=(b^2-3)
==>                _[2]=(a)
==>             [7]:
==>                _[1]=(3*b^2-1)
==>                _[2]=(a)
==>             [8]:
==>                _[1]=(b^4+5*b^2+8)
==>                _[2]=(a)
==>    [4]:
==>       r,p,y2,x2,y1,x1
==> [3]:
==>    [1]:
==>       _[1]=p
==>       _[2]=y2
==>       _[3]=x2
==>       _[4]=y1
==>       _[5]=x1
==>       _[6]=r^2
==>    [2]:
==>       _[1]=(10*a+b^4+44*b^2-16)*p+(b^4+44*b^2-16)*r+(-a*b^2+18*a)
==>       _[2]=(40*a+b^6+41*b^4-148*b^2+48)*y2+(a*b^3+32*a*b+2*b^5+88*b^3-32*\
   b)*r+(a*b^3+32*a*b+2*b^5+88*b^3-32*b)
==>       _[3]=(20*a+b^6+41*b^4-148*b^2+48)*x2+(a*b^2-8*a+2*b^4+88*b^2-32)*r+\
   (a*b^2+12*a+b^6+43*b^4-60*b^2+16)
==>       _[4]=(20*a+b^6+41*b^4-148*b^2+48)*y1+(2*b^5+88*b^3-32*b)*r+(-a*b^3-\
   32*a*b+2*b^5+88*b^3-32*b)
==>       _[5]=(a+b^6+41*b^4-148*b^2+48)*x1+(-2*b^4-88*b^2+32)*r+(3*a-b^6-43*\
   b^4+60*b^2-16)
==>       _[6]=(5*a+b^4+44*b^2-16)*r^2+(-10*a-2*b^4-88*b^2+32)*r+(-a*b^2-27*a\
   -b^6-44*b^4+16*b^2)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(a)
==>          [2]:
==>             [1]:
==>                _[1]=(b)
==>                _[2]=(a)
==>             [2]:
==>                _[1]=(b^2-3)
==>                _[2]=(a)
==>             [3]:
==>                _[1]=(3*b^2-1)
==>                _[2]=(a)
==>       [2]:
==>          [1]:
==>             _[1]=(b^4+44*b^2-16)
==>             _[2]=(5*a+b^2+7)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       p,y2,x2,y1,x1,r^2
==> [4]:
==>    [1]:
==>       _[1]=y2
==>       _[2]=y1
==>       _[3]=r^2
==>       _[4]=p^2
==>       _[5]=x1^2
==>    [2]:
==>       _[1]=y2
==>       _[2]=y1
==>       _[3]=r^2-2*r+(-a^2+2*a)
==>       _[4]=p^2+2*p+(-a^2-2*a)
==>       _[5]=x1^2-x2^2+2*x1+2*x2
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b)
==>          [2]:
==>             [1]:
==>                _[1]=(b)
==>                _[2]=(a-1)
==>             [2]:
==>                _[1]=(b)
==>                _[2]=(a+1)
==>    [4]:
==>       y2,y1,r^2,p^2,x1^2
==> [5]:
==>    [1]:
==>       _[1]=y2
==>       _[2]=x2
==>       _[3]=y1
==>       _[4]=x1
==>       _[5]=r^2
==>       _[6]=p^2
==>    [2]:
==>       _[1]=4*y2+(-3*b)*r+(-3*b)
==>       _[2]=4*x2-3*r+1
==>       _[3]=4*y1+(3*b)*p+(-3*b)
==>       _[4]=4*x1-3*p-1
==>       _[5]=3*r^2-6*r-1
==>       _[6]=3*p^2+6*p-1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(3*b^2-1)
==>             _[2]=(a)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       y2,x2,y1,x1,r^2,p^2
==> [6]:
==>    [1]:
==>       _[1]=r
==>       _[2]=p
==>       _[3]=y2
==>       _[4]=x2
==>       _[5]=y1
==>       _[6]=x1
==>    [2]:
==>       _[1]=r+1
==>       _[2]=p-1
==>       _[3]=2*y2+(-b)
==>       _[4]=2*x2+1
==>       _[5]=2*y1+(-b)
==>       _[6]=2*x1-1
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b^2-3)
==>             _[2]=(a)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       r,p,y2*@t,x2,y1*@t,x1,y1^2
==> [7]:
==>    [1]:
==>       _[1]=y1
==>       _[2]=r^2
==>       _[3]=y2*r
==>       _[4]=p^2
==>       _[5]=x1^2
==>    [2]:
==>       _[1]=y1
==>       _[2]=r^2-2*r-3
==>       _[3]=y2*r-3*y2
==>       _[4]=p^2+2*p+1
==>       _[5]=x1^2-x2^2-y2^2+2*x1+2*x2
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b)
==>             _[2]=(a+1)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       y1,r^2,y2*r,p^2,x1^2
==> [8]:
==>    [1]:
==>       _[1]=y2
==>       _[2]=r^2
==>       _[3]=p^2
==>       _[4]=y1*p
==>       _[5]=x1^2
==>    [2]:
==>       _[1]=y2
==>       _[2]=r^2-2*r+1
==>       _[3]=p^2+2*p-3
==>       _[4]=y1*p+3*y1
==>       _[5]=x1^2+y1^2-x2^2+2*x1+2*x2
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b)
==>             _[2]=(a-1)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       y2,r^2,p^2,y1*p,x1^2
==> [9]:
==>    [1]:
==>       _[1]=r
==>       _[2]=y2
==>       _[3]=x2
==>       _[4]=y1
==>       _[5]=x1
==>       _[6]=p^2
==>    [2]:
==>       _[1]=10*r+(b^2-18)
==>       _[2]=20*y2+(-b^3-32*b)
==>       _[3]=x2-3
==>       _[4]=40*y1+(-b^3-32*b)*p+(b^3+32*b)
==>       _[5]=20*x1+(b^2-8)*p+(-b^2-12)
==>       _[6]=5*p^2+10*p+(-b^2-27)
==>    [3]:
==>       [1]:
==>          [1]:
==>             _[1]=(b^4+44*b^2-16)
==>             _[2]=(5*a-b^2-7)
==>          [2]:
==>             [1]:
==>                _[1]=1
==>    [4]:
==>       r,y2,x2,y1,x1,p^2
==>  
int i;
list H;
for(i=1;i<=size(GC93);i++){H[i]=GC93[i][3];}
"H="; H;
==> H=
==> [1]:
==>    [1]:
==>       [1]:
==>          _[1]=0
==>       [2]:
==>          [1]:
==>             _[1]=(8*a^10+41*a^8*b^2-56*a^8+84*a^6*b^4-164*a^6*b^2+144*a^6\
   +86*a^4*b^6-148*a^4*b^4+86*a^4*b^2-176*a^4+44*a^2*b^8-28*a^2*b^6-148*a^2*\
   b^4+156*a^2*b^2+104*a^2+9*b^10+12*b^8-74*b^6-172*b^4+137*b^2-24)
==>          [2]:
==>             _[1]=(b)
==>          [3]:
==>             _[1]=(a)
==> [2]:
==>    [1]:
==>       [1]:
==>          _[1]=(8*a^10+41*a^8*b^2-56*a^8+84*a^6*b^4-164*a^6*b^2+144*a^6+86\
   *a^4*b^6-148*a^4*b^4+86*a^4*b^2-176*a^4+44*a^2*b^8-28*a^2*b^6-148*a^2*b^4\
   +156*a^2*b^2+104*a^2+9*b^10+12*b^8-74*b^6-172*b^4+137*b^2-24)
==>       [2]:
==>          [1]:
==>             _[1]=(b)
==>             _[2]=(a-1)
==>          [2]:
==>             _[1]=(b)
==>             _[2]=(a+1)
==>          [3]:
==>             _[1]=(b)
==>             _[2]=(a^2-3)
==>          [4]:
==>             _[1]=(b^4+44*b^2-16)
==>             _[2]=(5*a-b^2-7)
==>          [5]:
==>             _[1]=(b^4+44*b^2-16)
==>             _[2]=(5*a+b^2+7)
==>          [6]:
==>             _[1]=(b^2-3)
==>             _[2]=(a)
==>          [7]:
==>             _[1]=(3*b^2-1)
==>             _[2]=(a)
==>          [8]:
==>             _[1]=(b^4+5*b^2+8)
==>             _[2]=(a)
==> [3]:
==>    [1]:
==>       [1]:
==>          _[1]=(a)
==>       [2]:
==>          [1]:
==>             _[1]=(b)
==>             _[2]=(a)
==>          [2]:
==>             _[1]=(b^2-3)
==>             _[2]=(a)
==>          [3]:
==>             _[1]=(3*b^2-1)
==>             _[2]=(a)
==>    [2]:
==>       [1]:
==>          _[1]=(b^4+44*b^2-16)
==>          _[2]=(5*a+b^2+7)
==>       [2]:
==>          [1]:
==>             _[1]=1
==> [4]:
==>    [1]:
==>       [1]:
==>          _[1]=(b)
==>       [2]:
==>          [1]:
==>             _[1]=(b)
==>             _[2]=(a-1)
==>          [2]:
==>             _[1]=(b)
==>             _[2]=(a+1)
==> [5]:
==>    [1]:
==>       [1]:
==>          _[1]=(3*b^2-1)
==>          _[2]=(a)
==>       [2]:
==>          [1]:
==>             _[1]=1
==> [6]:
==>    [1]:
==>       [1]:
==>          _[1]=(b^2-3)
==>          _[2]=(a)
==>       [2]:
==>          [1]:
==>             _[1]=1
==> [7]:
==>    [1]:
==>       [1]:
==>          _[1]=(b)
==>          _[2]=(a+1)
==>       [2]:
==>          [1]:
==>             _[1]=1
==> [8]:
==>    [1]:
==>       [1]:
==>          _[1]=(b)
==>          _[2]=(a-1)
==>       [2]:
==>          [1]:
==>             _[1]=1
==> [9]:
==>    [1]:
==>       [1]:
==>          _[1]=(b^4+44*b^2-16)
==>          _[2]=(5*a-b^2-7)
==>       [2]:
==>          [1]:
==>             _[1]=1
"addcons(H)="; addcons(H);
==> addcons(H)=
==> [1]:
==>    [1]:
==>       1,1
==>    [2]:
==>       _[1]=0
==>    [3]:
==>       [1]:
==>          _[1]=1
==>    [5]:
==>       1

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